Displaying similar documents to “Algebraic non-integrability of the Cohen map.”

Some (non-)elimination results for curves in geometric structures

Serge Randriambololona, Sergei Starchenko (2011)

Fundamenta Mathematicae

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We show that the first order structure whose underlying universe is ℂ and whose basic relations are all algebraic subsets of ℂ² does not have quantifier elimination. Since an algebraic subset of ℂ² is either of dimension ≤ 1 or has a complement of dimension ≤ 1, one can restate the former result as a failure of quantifier elimination for planar complex algebraic curves. We then prove that removing the planarity hypothesis suffices to recover quantifier elimination: the structure with...

On algebraic solutions of algebraic Pfaff equations

Henryk Żołądek (1995)

Studia Mathematica

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We give a new proof of Jouanolou’s theorem about non-existence of algebraic solutions to the system ẋ = z s , ẏ = x s , ż = y s . We also present some generalizations of the results of Darboux and Jouanolou about algebraic Pfaff forms with algebraic solutions.

On the geometry of algebraic curves having many real components.

J. Huisman (2001)

Revista Matemática Complutense

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We show that there is a large class of nonspecial effective divisors of relatively small degree on real algebraic curves having many real components i.e. on M-curves. We apply to 1. complete linear systems on M-curves containing divisors with entirely real support, and 2. morphisms of M-curves into P1.